US7162393B1 - Detecting degradation of components during reliability-evaluation studies - Google Patents
Detecting degradation of components during reliability-evaluation studies Download PDFInfo
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- US7162393B1 US7162393B1 US11/219,091 US21909105A US7162393B1 US 7162393 B1 US7162393 B1 US 7162393B1 US 21909105 A US21909105 A US 21909105A US 7162393 B1 US7162393 B1 US 7162393B1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/28—Testing of electronic circuits, e.g. by signal tracer
- G01R31/2832—Specific tests of electronic circuits not provided for elsewhere
- G01R31/2836—Fault-finding or characterising
- G01R31/2849—Environmental or reliability testing, e.g. burn-in or validation tests
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F11/00—Error detection; Error correction; Monitoring
- G06F11/008—Reliability or availability analysis
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F11/00—Error detection; Error correction; Monitoring
- G06F11/22—Detection or location of defective computer hardware by testing during standby operation or during idle time, e.g. start-up testing
- G06F11/24—Marginal checking or other specified testing methods not covered by G06F11/26, e.g. race tests
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- the present invention relates to techniques for determining the reliability of a component in a system. More specifically, the present invention relates to a method and apparatus for determining the reliability of a component by identifying the onset of hardware degradation during an accelerated-life study of the component.
- determining the reliability of a component can be very time consuming if reliability testing is performed under normal operating conditions. This is because, under normal conditions, a highly reliable component can take an inordinate amount of time to fail.
- reliability-evaluation studies can include “accelerated-life studies,” which accelerate the failure mechanisms of a component, or burn-in studies, which determine if a particular component is functioning properly prior to being shipped to customers.
- These types of studies subject the component to stressful conditions, typically using environmental stress-test chambers to hold and/or cycle one or more stress variables (e.g. temperature, humidity, radiation flux, etc.) at levels that are believed to accelerate subtle failure mechanisms within the component.
- stress variables e.g. temperature, humidity, radiation flux, etc.
- One embodiment of the present invention provides a system that determines the reliability of a component in a system.
- the system monitors inferential variables associated with a number of specimens of the component.
- the system collects degradation data by first computing a likelihood value that indicates whether an inferential variable associated with a specimen of the component is behaving normally or abnormally.
- the system determines whether the specimen of the component has degraded based on the likelihood value. If the specimen of the component is determined to have degraded, the system records the time when the specimen of the component was determined to have degraded.
- the system also uses the degradation data to determine the reliability of the component in the system.
- the system determines whether the specimen of the component has degraded by first comparing the likelihood value with an upper threshold and comparing the likelihood value with a lower threshold. If the likelihood value is greater than or equal to the upper threshold, the system determines that the specimen of the component has degraded. If the likelihood value is less than or equal to the lower threshold, the system determines that the specimen of the component is behaving normally. If the likelihood value is between the upper threshold and the lower threshold, the system determines that an inadequate amount of information is available to determine whether the specimen of the component is behaving normally or whether the specimen of the component has degraded.
- the system computes the likelihood value by first computing the probability that a null hypothesis is true based on a current value of the inferential variable and historical values of the inferential variable. Note that the null hypothesis is true if the specimen of the component is behaving normally and has not degraded. Next, the system computes the probability that an alternative hypothesis is true using the current value of the inferential variable and historical values of the inferential variable. Note that the alternative hypothesis is true if the specimen of the component has degraded. The system then computes the likelihood value by dividing the probability that the alternative hypothesis is true by the probability that the null hypothesis is true.
- the alternative hypothesis test can include: a positive-mean test, which tests whether the mean of a time-series for the inferential variable is above a reference level; a negative-mean test, which tests whether the mean of the time-series for the inferential variable is below a reference level; a nominal-variance test, which tests whether the variance of the time-series for the inferential variable is proportional to a scale factor; a inverse-variance test, which tests whether the variance of the time-series for the inferential variable is proportional to the inverse of the scale factor; a positive first-difference test, which tests whether the time-series for the inferential variable is increasing; or a negative first-difference test, which tests whether the time-series for the inferential variable is decreasing.
- a positive-mean test which tests whether the mean of a time-series for the inferential variable is above a reference level
- a negative-mean test which tests whether the mean of the time-series for the
- the system prior to monitoring an inferential variable, computes the mean and the variance of the time-series for the inferential variable by monitoring the inferential variable during a training phase.
- the mean and variance are then used to normalize the mean and the variance of the time-series for the inferential variable while monitoring the inferential variable during the monitoring phase.
- the inferential variable can represent a current passing through the component or a voltage applied to the component.
- the inferential variable is monitored during an accelerated-life study of the component.
- the monitored data can be processed in real-time or can be post-processed.
- FIG. 1 illustrates an accelerated-life stress-test chamber in accordance with an embodiment of the present invention.
- FIG. 2 presents a flow chart illustrating the process of detecting the onset of hardware degradation for components undergoing accelerated-life studies in accordance with an embodiment of the present invention
- a computer-readable storage medium which may be any device or medium that can store code and/or data for use by a computer system.
- the transmission medium may include a communications network, such as the Internet.
- FIG. 1 illustrates accelerated-life stress-test chamber 100 in accordance with an embodiment of the present invention. It contains a plurality of components under stress-test, including components 102 , 104 , 106 , and 108 . Stress-test chamber 100 provides individual signal outputs for each component under test. The signal outputs from each component can include current, voltage, temperature, and other physical variables. Note that components 102 , 104 , 106 , and 108 are tested at the same time under the same conditions. Also note that instead of testing multiple individual components, the stress-test chamber can be configured to test a single computer system.
- One embodiment of the present invention integrates an ultra-sensitive sequential detection algorithm called the Sequential Probability Ratio Test (SPRT) for inferential variable surveillance to accurately identify the onset of component degradation and/or failure.
- SPRT Sequential Probability Ratio Test
- a tandem SPRT can be run on the derivative of the inferential variable's time series to accurately assess the point of failure.
- the combination of tandem SPRTs that monitor the inferential variables provides a robust surveillance scheme that has the capability to:
- information from the tandem SPRT analyses is combined with discrete-time ex-situ pass/fail testing to construct a detailed population failure distribution.
- the present invention lessens the constraints on the tradeoff between the number of units under test and the duration of the experiments, while yielding much higher resolution information on the dynamic evolution of the health of the components as a function of age and cumulative stress. This higher resolution enables higher confidence in selecting a mathematical model that accurately predicts the long-term reliability of the component for a time point beyond the number of hours the component was actually tested.
- the Sequential Probability Ratio Test is a statistical hypothesis test that differs from standard fixed sample tests. In fixed-sample statistical tests, a given number of observations are used to select one hypothesis from one or more alternative hypotheses. The SPRT, however, examines one observation at a time, and then makes a decision as soon as it has sufficient information to ensure that pre-specified confidence bounds are met.
- the basic approach taken by the SPRT technique is to analyze successive observations of a discrete process.
- y n represent a sample from the process at a given moment t n in time.
- PDF white-noise probability density function
- the SPRT is a binary hypothesis test that analyzes process observations sequentially to determine whether or not the signal is consistent with normal behavior. When a SPRT reaches a decision about current process behavior (i.e. the signal is behaving normally or abnormally), the system reports the decision and continues to process observations.
- the signal data adheres to a Gaussian PDF with mean 0 and variance ⁇ 2 for normal signal behavior, referred to as the null hypothesis, H 0 .
- the system computes six specific SPRT hypothesis tests in parallel for each inferential variable monitored.
- One embodiment of the present invention applies a SPRT to an electrical current time-series.
- Other embodiments of the present invention apply a SPRT to other inferential variables, including voltage, internal temperature, or stress variables.
- the signal data for the corresponding alternative hypothesis, H 3 adheres to a Gaussian PDF with mean 0 and variance V ⁇ 2 (with scalar factor V).
- the signal data for the corresponding alternative hypothesis, H 4 adheres to a Gaussian PDF with mean 0 and variance ⁇ 2 /V.
- the final two tandem SPRT tests are performed not on the raw inferential variables as above, but on the first difference function of the inferential variable.
- the first difference function i.e. difference between each observation and the observation preceding it
- the observations in the first difference function are a nominally stationary random process centered about zero. If an upward or downward trend suddenly appears in the signal, SPRTs number 5 and 6 observe an increase or decrease, respectively, in the slope of the inferential variable.
- SPRT alarms are triggered for SPRTs 2 and 6 .
- SPRT 2 generates a warning because the sequence of raw observations drops with time.
- SPRT 6 generates a warning because the slope of the inferential variable changes from zero to something less than zero.
- the advantage of monitoring the mean SPRT and slope SPRT in tandem is that the system correlates the SPRT readings from the six tests and determines if the component has failed. For example, if the signal levels off to a new stationary value (or plateau), the alarms from SPRT 6 cease because the slope returns to zero when the raw signal reaches a plateau. However, SPRT 2 will continue generating a warning because the new mean value of the signal is different from the value prior to the degradation. Therefore, the system correctly identifies that the component has failed.
- the variance of the inferential variable is either increasing or decreasing, respectively.
- An increasing variance that is not accompanied by a change in mean signifies an episodic event that is “bursty” or “spiky” with time.
- a decreasing variance that is not accompanied by a change in mean is a common symptom of a failing component that is characterized by an increasing time constant. Therefore, having variance SPRTs available in parallel with slope and mean SPRTs provides a wealth of supplementary diagnostic information that has not been possible with conventional accelerated-life studies.
- the SPRT technique provides a quantitative framework that permits a decision to be made between the null hypothesis and the six alternative hypotheses with specified misidentification probabilities. If the SPRT accepts one of the alternative hypotheses, an alarm flag is set and data is transmitted.
- the SPRT operates as follows. At each time step in a calculation, the system calculates a test index and compares it to two stopping boundaries A and B (defined below).
- the test index is equal to the natural log of a likelihood ratio (L n ), which for a given SPRT is the ratio of the probability that the alternative hypothesis for the test (H j , where j is the appropriate subscript for the SPRT in question) is true, to the probability that the null hypothesis (H 0 ) is true.
- L n probability ⁇ ⁇ of ⁇ ⁇ observed ⁇ ⁇ sequence ⁇ ⁇ ⁇ Y n ⁇ ⁇ ⁇ given ⁇ ⁇ H j ⁇ ⁇ is ⁇ ⁇ true probability ⁇ ⁇ of ⁇ ⁇ observed ⁇ ⁇ sequence ⁇ ⁇ ⁇ Y n ⁇ ⁇ ⁇ given ⁇ ⁇ H 0 ⁇ ⁇ is ⁇ ⁇ true ( 1 )
- the logarithm of the likelihood ratio is greater than or equal to the logarithm of the upper threshold limit [i.e., ln(L n )>ln(B)], then the alternative hypothesis is true. If the logarithm of the likelihood ratio is less than or equal to the logarithm of the lower threshold limit [i.e., ln(L n ) ⁇ ln(A)], then the null hypothesis is true. If the log likelihood ratio falls between the two limits, [i.e., ln(A) ⁇ ln(L n ) ⁇ ln(B)], then there is not enough information to make a decision (and, incidentally, no other statistical test could yet reach a decision with the same given Type I and II misidentification probabilities).
- ⁇ is the probability of accepting H j when H 0 is true (i.e., the false-alarm probability)
- ⁇ is the probability of accepting H 0 when H j is true (i.e., the missed-alarm probability).
- the first two SPRT tests for normal distributions examine the mean of the process observations. If the distribution of observations exhibits a non-zero mean (e.g., a mean of either +M or ⁇ M, where M is the pre-assigned system disturbance magnitude for the mean test), the mean tests determine that the system is degraded. Assuming that the sequence ⁇ Y n ⁇ adheres to a Gaussian PDF, then the probability that the null hypothesis H 0 is true (i.e., mean 0 and variance ⁇ 2 ) is:
- a non-zero mean e.g., a mean of either +M or ⁇ M, where M is the pre-assigned system disturbance magnitude for the mean test
- SPRT neg The SPRT index for the negative-mean test (SPRT neg ) is derived by substituting ⁇ M for each instance of M in (4) through (6) above, resulting in:
- the likelihood ratio for the variance test is given by the ratio of (8) to (3):
- SPRT inv The SPRT index for the inverse-variance test (SPRT inv ) is derived by substituting 1/V for each instance of V in (8) through (10), resulting in:
- the tandem SPRT module performs mean, variance, and SPRT tests on the raw process signal and on its first difference function.
- the user specifies the system disturbance magnitudes for the tests (M and V), the false-alarm probability ( ⁇ ), and the missed-alarm probability ( ⁇ ).
- the module calculates the mean and variance of the monitored variable process signal.
- the mean of the raw observations for the inferential variable will be nonzero; in this case the mean calculated from the training phase is used to normalize the signal during the monitoring phase.
- the system disturbance magnitude for the mean tests specifies the number of standard deviations (or fractions thereof) that the distribution must shift in the positive or negative direction to trigger an alarm.
- the system disturbance magnitude for the variance tests specifies the fractional change of the variance necessary to trigger an alarm.
- the system sets all six SPRT indices to 0. Then, during each time step of the calculation, the system updates the SPRT indices using (6), (7), (10), and (11). The system compares each SPRT index is then compared to the upper [i.e., ln((1 ⁇ )/ ⁇ ] and lower [i.e., ln(( ⁇ /(1 ⁇ ))] decision boundaries, with these three possible outcomes:
- the present invention uses tandem SPRTs to monitor “derivative SPRTs” in parallel with mean and variance SPRTs that are performed on the time-series associated an inferential variable in the context of accelerated-life studies, where it is not possible to perform direct functional tests in real-time.
- the new tandem-SPRT approach facilitates determining the onset of hardware degradation for components under test as well as the exact time of failure (within the resolution of the time samples used for sampling the referential variable).
- the onset of “spiky” degradation in components as well as degradation in the sensor that is used to measure the inferential variable can be deduced.
- Information from the suite of six tandem SPRTs provides a substantially complete and substantially accurate picture of the dynamic reliability of the components under test as a function of age and cumulative stress.
- FIG. 2 presents a flow chart illustrating the process of detecting the onset of hardware degradation for components undergoing accelerated-life studies in accordance with an embodiment of the present invention.
- the system monitors an inferential variable (step 202 ).
- the system computes a probability that the null hypothesis test is true (step 204 ) and computes the probability that an alternative hypothesis test is true (step 206 ). Recall that the null hypothesis is true if the specimen of the component is behaving normally and has not degraded. Conversely, the alternative hypothesis is true if the specimen of the component has degraded.
- the system then computes a likelihood ratio by taking the ratio of the probability that the alternative hypothesis test is true to the probability that the null hypothesis tests is true (step 208 ).
- the system compares the likelihood ratio to an upper threshold and a lower threshold (step 210 ). Note that these thresholds allow the user to tune the sensitivity of the process while detecting abnormal behavior of an inferential variable.
- the system determines that the component has degraded (step 214 ) and records the time at which the component has degraded (step 216 ). The system then continues monitoring the inferential variable (step 218 ).
- the system determines that the inferential variable is observing background variations (step 222 ) and continues monitoring the inferential variable (step 218 ).
Abstract
Description
-
- 1. detect the onset of degradation in any individual component under stress, even when the overall functionality of that component cannot be measured directly; and to
- 2. detect the time of complete failure for any component under stress.
where α is the probability of accepting Hj when H0 is true (i.e., the false-alarm probability), and β is the probability of accepting H0 when Hj is true (i.e., the missed-alarm probability).
-
- 1. the lower limit is reached, in which case the process is declared healthy, the test statistic is reset to zero, and sampling continues;
- 2. the upper limit is reached, in which case the process is declared degraded, an alarm flag is raised indicating a sensor or process fault, the test statistic is reset to zero, and sampling continues; or
- 3. neither limit has been reached, in which case no decision concerning the process can yet be made, and the sampling continues.
-
- 1. early detection of very subtle anomalies in noisy process variables; and
- 2. pre-specification of quantitative false-alarm and missed-alarm probabilities.
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US20080056545A1 (en) * | 2006-09-05 | 2008-03-06 | Canon Kabushiki Kaisha | Image processing apparatus, image processing method, program for image processing method and its storage medium |
US20080114567A1 (en) * | 2006-11-03 | 2008-05-15 | Jeske Daniel R | Sequential sampling within a portable computing environment |
US20080255785A1 (en) * | 2007-04-16 | 2008-10-16 | Gross Kenny C | Length-of-the-curve stress metric for improved characterization of computer system reliability |
US20090106600A1 (en) * | 2007-10-17 | 2009-04-23 | Sun Microsystems, Inc. | Optimal stress exerciser for computer servers |
US20100010845A1 (en) * | 2008-07-10 | 2010-01-14 | Palo Alto Research Center Incorporated | Methods and systems for constructing production plans |
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